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Chapter 30: Q. 34 (page 871)

What value of resistor $R$ gives the circuit in FIGURE $EX 30.34$ a time constant of $25 渭蝉$ $?$

Short Answer

Expert verified

Value of resistor with time constant $25 渭蝉$ is $750 惟$ .

Step by step solution

01

Formula for current decays and equivalent resistance

In a circuit, current decays through an inductor, and the time constant is given by

$蟿 = \frac{L}{R_{eq}} . . . . . . . . . . 1$

R_{eq}

is the circuit's equivalent resistance

localid="1648830639011" $R_{eq} = \frac{L}{蟿} . . . . . . 2$

02

Calculation for resistance value

$L = 7.5 脳 10^{- 3} H$

$t = 25 脳 10^{- 6} s$

All values should be substituted,

$R_{eq} = \frac{L}{蟿} = \frac{7.5 脳 10^{- 3}}{25 脳 10^{- 6} s} = 300 惟$

The two resistors $500 惟$ and $R$ They are linked in a series.

Simultaneously, the corresponding resistance is equal to

$R = {(\frac{1}{R_{eq}} - \frac{1}{500 惟})}^{- 1}$

$= {(\frac{1}{300 惟} - \frac{1}{500 惟})}^{- 1}$

$= 750 惟$

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Most popular questions from this chapter

The maximum allowable potential difference across a 200 mH inductor is 400 V. You need to raise the current through the inductor from 1.0 A to 3.0 A. What is the minimum time you should allow for changing the current?

The earth's magnetic field strength is $5.0 脳 10^{鈭� 5} T$ . How fast would you have to drive your car to create a $1.0 V$ motional emf along your $1.0 鈭� m$ -tall radio antenna? Assume that the motion of the antenna is perpendicular to $\overset{鈫�}{B}$ .

56. II Your camping buddy has an idea for a light to go inside your CALC tent. He happens to have a powerful (and heavy!) horseshoe magnet that he bought at a surplus store. This magnet creates a $0.20$ T field between two pole tips $10 cm$ apart. His idea is to build the hand-cranked generator shown in FIGURE P30.56. He thinks you can make enough current to fully light a $1.0 惟$ lightbulb rated at $4.0 W$ . That's not super bright, but it should be plenty of light for routine activities in the tent.

a. Find an expression for the induced current as a function of time if you turn the crank at frequency f Assume that the semicircle is at its highest point at $t = 0 s$ .

b. With what frequency will you have to turn the crank tor the maximum current to fully light the bulb? Is this feasible?

A $20 cm 脳 20 cm$ square loop has a resistance of $0.10 惟$ . A CALC magnetic field perpendicular to the loop is $B = 4 t - 2 t^{2}$ , where $B$ is in Tesla and $t$ is in seconds. What is the current in the loop at $t = 0.0 s, t = 1.0 s$ ,and $t = 2.0 s ?$

11. a. Can you tell which of the inductors in FIGURE Q30.11 has the larger current through it? If so, which one? Explain.

b. Can you tell through which inductor the current is changing more rapidly? If so, which one? Explain.

c. If the current enters the inductor from the bottom, can you tell if the current is increasing, decreasing, or staying the same? If so, which? Explain.

FIGURE Q30.11

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